- Education and Science
The Best Math Tricks
Techniques You Can Use To Perform Math Quickly
Yes, that's right, here are quick-to-learn methods...ones that take only a minute to learn, that you can pick up and remember for the rest of your life. By reading only a few paragraphs of this article, you'll be amazed at what you can do.
Most of us want to run to a calculator. Many of us hate math. So what do you do when your options are limited?
Well, here's an additional option. Learn some techniques that make math easy.
The purpose of this article is to provide easy and quick techniques of mathematics. This means addition, subtraction, multiplication, and division.
Quickly Add A Consecutive List of Numbers
Example: Add all numbers from 1 to 20.
Note: This is also known as the summation of a series of numbers.
- Add the first and last number.
- Divide result by 2.
- Multiply result by the total of numbers in the list.
Applied Example: Add all numbers from 4 to 10.
- 4 + 10 = 14.
- 14 / 2 = 7.
- 7 X 7 = 49 (Since 4 to 10 involves 7 numbers).
Squaring A Number That Ends In 5 -- Super FAST!
Takes Less That 10 Seconds.
- Multiply the first digit of the number by itself plus 1.
- Insert the number "25" to the end of the result.
Example 1: The Square of 15.
- The first digit of 15 is "1", therefore multiply 1 X (1 + 1), or 1 X 2. The result is 2.
- Insert "25" at the end of the number. In this case, the result becomes 2...25, or "225".
- The first digit is "4", therefore 4 X 5 = 20.
- Insert "25" at the end of "20" to arrive at "2025".
Multiplying by 9 Without Trying
Surprisingly Sneakiness By Using 10.
When you multiply a number by 9, all you have to do is figet the numbers and you'll quickly resolve the problem. Do the following:
- Multiply the number by 10.
- Subtract the original number from your result; this will be your answer.
- 28 X 10 = 280.
- 280 - 28 = 252. This is the answer.
Testing for Divisibility -- 2
Can The Number Be Divided Evenly.
Sometimes, were are interested in finding out how to divide something up equally, with nothing left over. Using the following methods, you can quickly determine this.
Divisible by 2
If the number is even, it is divisible by 2. Most people already know this and apply this method.
Testing For Divisibility -- 3, 6, or 9
Divisible by 3
- Add the digits of the number together.
- If the result is divisible by 3, then the original number is divisible by 3.
Special Note: You can also cast out numbers automatically divisible by 3 (3, 6, and 9) to make this quicker when checking large numbers.
Example: Using the number 3, 465, 899, 622. Cast out 3, 6, 9, 9, and 6, then add 4 + 5 + 8 + 2 + 2 = 21. So this number is divisible by 3.
Divisible by 6
- First observe if the number is an even number.
- If the number is even, test it for divisibility by 3.
- If the number is even and divisible by 3, it is divisible by 6.
Divisible by 9
- Sum the digits of the number.
- If the result is divisible by 9, the original number is also divisible by 9.
Special Note: You can cast the "9"s out of a number to perform this calculation quicker. For example, 9,998,199 would be 8 + 1 = 9, and is therefore divisible by 9.
Testing For Divisibility -- 4 or 8
Divisible by 4
- Look at the last two digits of the number.
- If the result is divisible by 4, or is "00", then the number is divisible by 4.
Example 2: Using the number 316. Since the last two digits are "16", this number is divisible by 4.
Divisible by 8
- Look at the last three digits of the number.
- If the result is "000" or a number evenly divisible by 8, then the original number also divides evenly by 8.
Example 2: The number 425,512 is evenly divisible by 8 because "512" is divisible by 8.
An Alternate Technique for 4 and 8
An additional technique that reduces their calculations is by dividing the number in half, two times in a row:
- If number divides evenly, two times in a row, it is divisible by 4 (and, simultaneously, you have the result).
- If each result is an even number, then the original number is also divisible by 8.
- 36 divided by 2 is 18.
- 18 divided by 2 is 9. Therefore 36 is divisible by 4 (and the answer is 9).
- 512 divided in half is 256 (an even number).
- 256 divided in half is 128 (an even number).
- Therefore, 512 is divisible by 8.
Testing For Divisibility -- 5 or 10
Divisible by 5
If the number ends in a 5 or 0, it is divisible by 5.
Divisible by 10
If the number has two or more digits, and ends in a zero, it is divisible by 10.
These observations are already used by most of us.
Dividing Fractions -- The Simple Way
Note: You will need prior knowledge of multiplying fractions to complete this technique.
To Divide a Fraction
- Flip the second fraction.
- Then multiply the fractions.
Example 1/2 Ã· 1/3
- Switch 1/3 to "3/1".
- Multiply 1/2 and 3/1.
- The answer is "3/2", or 1 1/2
If you know of any math tricks, really good ones, or have comments concerning any of the tricks displayed here, please give me feedback. I'll be adding additional techniques from time to time, keeping this article alive.